Question: Rewrite as a simplified fraction. ${0.5\overline{56} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 556.5656...\\ 10x &= 5.5656...\end{align*}}$ Subtracting the two equations, we have: ${990x = 551}$ ${x = \dfrac{551}{990}} $